MOXVaporPressure

Parsed Function Material with automatic derivatives.

Description

Vapor pressure, which is a component of the pore velocity calculation is performed by the [MOXVaporPressure]class.

Specifically, $var element = document.getElementById("moose-equation-42936972-4404-476a-b3d2-79ff9ec687ff");katex.render("P", element, {displayMode:false,throwOnError:false});$ is the summation of the vapor pressure terms from the following fuel constituents: UO $var element = document.getElementById("moose-equation-ca111c5d-5e66-4896-9729-d02781833a59");katex.render("_{2}", element, {displayMode:false,throwOnError:false});$ , PuO2, UO, U, UO $var element = document.getElementById("moose-equation-7817e8c6-83a2-4c0f-a0ed-dfde05f1527a");katex.render("_3", element, {displayMode:false,throwOnError:false});$ , PuO, Pu, AmO $var element = document.getElementById("moose-equation-d02cfeb5-840d-4d47-8562-660c96c11f32");katex.render("_2", element, {displayMode:false,throwOnError:false});$ , Am, AmO, and O $var element = document.getElementById("moose-equation-55cc8243-34c2-4038-bd26-0615f0038bcd");katex.render("_2", element, {displayMode:false,throwOnError:false});$ . For $var element = document.getElementById("moose-equation-01db7e26-43e6-468a-a952-b62bfc74876b");katex.render("q", element, {displayMode:false,throwOnError:false});$ = Pu concentration, $var element = document.getElementById("moose-equation-08db1bed-9f85-4464-acf6-f356028fea51");katex.render("r", element, {displayMode:false,throwOnError:false});$ = Am concentration, $var element = document.getElementById("moose-equation-374fbb46-7a9d-466d-8942-21080b654f70");katex.render("x", element, {displayMode:false,throwOnError:false});$ = deviation from stoichiometry of the metal oxide (MO $var element = document.getElementById("moose-equation-622f817c-9762-4c07-99f1-70e0fb10a499");katex.render("_{2.00 - x}", element, {displayMode:false,throwOnError:false});$ ), $var element = document.getElementById("moose-equation-f8881e87-d909-4fba-8a3e-256c4871b388");katex.render("p\\_O_{2}", element, {displayMode:false,throwOnError:false});$ = partial pressure of oxygen (which is calculated in MOXOxygenPartialPressure along with its integral with respect to the O/M ratio), and Gibbs free energy via the Rand-Markin model ( $var element = document.getElementById("moose-equation-a396cc46-1ec9-4ba3-b775-1b8eefc0b87f");katex.render("\\Delta G", element, {displayMode:false,throwOnError:false});$ s defined subsequently), the following equations are the vapor pressure terms as a function of temperature ( $var element = document.getElementById("moose-equation-77b5b55c-e1d8-44ee-ada6-95170c641f76");katex.render("T", element, {displayMode:false,throwOnError:false});$ ), from Ikusawa et al. (2014) (with corrections from the authors): $var element = document.getElementById("moose-equation-5b8d1e87-7d3a-4e2b-b6ea-32fb7fb135f1");katex.render("\\begin{aligned} p\\_UO_{2} = (1-q-r) \\text{ } \\text{exp}\\left(-\\frac{\\Delta G_{UO_{2},\\text{vap}}}{RT}\\right)\\\\ \\text{ }\\\\ p\\_PuO_{2} = q \\text{ } (p\\_O_{2})^{m/2}\\text{exp}\\left(-\\frac{\\Delta G_{A}}{RT}\\right)\\\\ \\text{ }\\\\ p\\_UO = \\frac{p\\_UO_{2}}{\\text{exp}\\left(-\\frac{\\Delta G_{UO/UO_{2}}}{RT}\\right) (p\\_O_{2})^{1/2}}\\\\ \\text{ }\\\\ p\\_U = \\frac{p\\_UO}{\\text{exp}\\left(-\\frac{\\Delta G_{U/UO}}{RT}\\right) (p\\_O_{2})^{1/2}}\\\\ \\text{ }\\\\ p\\_UO_{3} = p\\_UO_{2} \\text{ } (p\\_O_{2})^{1/2} \\text{ } \\text{exp}\\left(-\\frac{\\Delta G_{UO_{2}/UO_{3}}}{RT}\\right) \\\\ \\text{ }\\\\ p\\_PuO = \\frac{p\\_PuO_{2}}{\\text{exp}\\left(-\\frac{\\Delta G_{PuO/PuO_{2}}}{RT}\\right) (p\\_O_{2})^{1/2}}\\\\ \\text{ }\\\\ p\\_Pu = \\frac{p\\_PuO}{\\text{exp}\\left(-\\frac{\\Delta G_{Pu/PuO_{2}}}{RT}\\right) (p\\_O_{2})^{1/2}}\\\\ \\text{ }\\\\ p\\_AmO_{2} = r \\text{ } (p\\_O_{2})^{n/2} \\text{ } \\text{exp}\\left(-\\frac{\\Delta G_{B}}{RT}\\right) \\\\ \\text{ }\\\\ p\\_Am = \\frac{p\\_AmO_{2}}{\\text{exp}\\left(-\\frac{\\Delta G_{AmO_{2}/Am}}{RT}\\right) p\\_O_{2}}\\\\ \\text{ }\\\\ p\\_AmO = p\\_Am \\text{ } (p\\_O_{2})^{1/2} \\text{ } \\text{exp}\\left(-\\frac{\\Delta G_{AmO/Am}}{RT}\\right) \\\\ \\text{ }\\\\ \\Delta G_{A} = -\\frac{1}{2}\\int_0^m \\! RT \\text{ }\\text{ln}(p\\_O_{2}) \\, \\mathrm{d}x + \\Delta G_{PuO_{2},\\text{vap}}\\\\ \\text{ }\\\\ \\Delta G_{B} = -\\frac{1}{2}\\int_0^n \\! RT \\text{ }\\text{ln}(p\\_O_{2}) \\, \\mathrm{d}x + \\Delta G_{AmO_{2},\\text{vap}}\\\\ \\text{ }\\\\ m = \\frac{x}{q}\\\\ \\text{ }\\\\ n = \\frac{x}{r} \\end{aligned}", element, {displayMode:true,throwOnError:false});$

The Gibbs free energy depends on the chemistry of the fuel: $var element = document.getElementById("moose-equation-dfed955a-a5e6-4767-a3d5-458c52884236");katex.render("\\begin{aligned} \\Delta G_{UO_{2},\\text{vap}} = 567000 - 150T \\text{ }\\\\ \\Delta G_{PuO_{2},\\text{vap}} = 571000 - 150T \\text{ }\\\\ \\Delta G_{UO/UO_{2}} = -471000 + 71T \\text{ }\\\\ \\Delta G_{U/UO} = -528000 + 62T \\text{ }\\\\ \\Delta G_{UO_{2}/UO_3} = -404000 + 90T \\text{ }\\\\ \\Delta G_{PuO/PuO_{2}} = -352000 + 69T \\text{ }\\\\ \\Delta G_{Pu/PuO} = -498000 + 46T \\text{ }\\\\ \\Delta G_{AmO_2,\\text{vap}} = -R \\text{ } T \\text{ } ln(10^{(7.28-28260T)}) \\text{ }\\\\ \\Delta G_{AmO/Am} = (-137700 - 28.8T) - (263650 - 112.32T) \\text{ }\\\\ \\Delta G_{AmO_2/Am} = (-388300 + 30.7T) - (263650 - 112.32T) \\end{aligned}", element, {displayMode:true,throwOnError:false});$

The pressure that goes into the velocity calculation in MOXPoreVelocityVaporPressure is the sum of these individual vapor pressures: $var element = document.getElementById("moose-equation-8d12091b-f2b4-4157-8cef-03d22606d010");katex.render("\\begin{aligned} P & = p\\_UO_{2} + p\\_PuO_{2} + p\\_UO + p\\_U + p\\_UO_{3} \\\\ & + p\\_PuO + p\\_Pu + p\\_AmO_{2} + p\\_Am + p\\_AmO \\end{aligned}", element, {displayMode:true,throwOnError:false});$ and the derivative of this term with respect to temperature ( $var element = document.getElementById("moose-equation-008f71a7-87f8-4b53-9748-d1bff616618f");katex.render("\\frac{dP}{dT}", element, {displayMode:false,throwOnError:false});$ ) is also used in MOXPoreVelocityVaporPressure

construction

This class is still under development!

See bison/test/mox_pore_velocity/ for examples of how this class should be used.

Input Parameters

temperatureCoupled Temperature
C++ Type:std::vector<VariableName>
Unit:(no unit assumed)
Controllable:No
Description:Coupled Temperature

Required Parameters

additional_derivative_symbolsA list of additional (non-variable) symbols (such as material property or postprocessor names) to take derivatives w.r.t.
C++ Type:std::vector<std::string>
Controllable:No
Description:A list of additional (non-variable) symbols (such as material property or postprocessor names) to take derivatives w.r.t.
blockThe list of blocks (ids or names) that this object will be applied
C++ Type:std::vector<SubdomainName>
Controllable:No
Description:The list of blocks (ids or names) that this object will be applied
boundaryThe list of boundaries (ids or names) from the mesh where this object applies
C++ Type:std::vector<BoundaryName>
Controllable:No
Description:The list of boundaries (ids or names) from the mesh where this object applies
computeTrueWhen false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
Default:True
C++ Type:bool
Controllable:No
Description:When false, MOOSE will not call compute methods on this material. The user must call computeProperties() after retrieving the MaterialBase via MaterialBasePropertyInterface::getMaterialBase(). Non-computed MaterialBases are not sorted for dependencies.
constant_onNONEWhen ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
Default:NONE
C++ Type:MooseEnum
Options:NONE, ELEMENT, SUBDOMAIN
Controllable:No
Description:When ELEMENT, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps.When SUBDOMAIN, MOOSE will only call computeQpProperties() for the 0th quadrature point, and then copy that value to the other qps. Evaluations on element qps will be skipped
declare_suffixAn optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any declared properties. The suffix will be prepended with a '_' character.
derivative_order3Maximum order of derivatives taken
Default:3
C++ Type:unsigned int
Controllable:No
Description:Maximum order of derivatives taken
epsilon0Fuzzy comparison tolerance
Default:0
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Fuzzy comparison tolerance
error_on_missing_material_propertiesTrueThrow an error if any explicitly requested material property does not exist. Otherwise assume it to be zero.
Default:True
C++ Type:bool
Controllable:No
Description:Throw an error if any explicitly requested material property does not exist. Otherwise assume it to be zero.
extra_symbolsSpecial symbols, like point coordinates, time, and timestep size.
C++ Type:MultiMooseEnum
Options:x, y, z, t, dt
Controllable:No
Description:Special symbols, like point coordinates, time, and timestep size.
property_namePsumName of the parsed material property
Default:Psum
C++ Type:std::string
Controllable:No
Description:Name of the parsed material property
q0.2Pu concentration
Default:0.2
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Pu concentration
r0.05Am concentration
Default:0.05
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:Am concentration
upstream_materialsList of upstream material properties that must be evaluated when compute=false
C++ Type:std::vector<MaterialName>
Controllable:No
Description:List of upstream material properties that must be evaluated when compute=false
x0.02MOX deviation
Default:0.02
C++ Type:double
Unit:(no unit assumed)
Controllable:No
Description:MOX deviation

Optional Parameters

control_tagsAdds user-defined labels for accessing object parameters via control logic.
C++ Type:std::vector<std::string>
Controllable:No
Description:Adds user-defined labels for accessing object parameters via control logic.
enableTrueSet the enabled status of the MooseObject.
Default:True
C++ Type:bool
Controllable:Yes
Description:Set the enabled status of the MooseObject.
implicitTrueDetermines whether this object is calculated using an implicit or explicit form
Default:True
C++ Type:bool
Controllable:No
Description:Determines whether this object is calculated using an implicit or explicit form
seed0The seed for the master random number generator
Default:0
C++ Type:unsigned int
Controllable:No
Description:The seed for the master random number generator
use_displaced_meshFalseWhether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.
Default:False
C++ Type:bool
Controllable:No
Description:Whether or not this object should use the displaced mesh for computation. Note that in the case this is true but no displacements are provided in the Mesh block the undisplaced mesh will still be used.

Advanced Parameters

disable_fpoptimizerFalseDisable the function parser algebraic optimizer
Default:False
C++ Type:bool
Controllable:No
Description:Disable the function parser algebraic optimizer
enable_ad_cacheTrueEnable caching of function derivatives for faster startup time
Default:True
C++ Type:bool
Controllable:No
Description:Enable caching of function derivatives for faster startup time
enable_auto_optimizeTrueEnable automatic immediate optimization of derivatives
Default:True
C++ Type:bool
Controllable:No
Description:Enable automatic immediate optimization of derivatives
enable_jitTrueEnable just-in-time compilation of function expressions for faster evaluation
Default:True
C++ Type:bool
Controllable:No
Description:Enable just-in-time compilation of function expressions for faster evaluation
evalerror_behaviornanWhat to do if evaluation error occurs. Options are to pass a nan, pass a nan with a warning, throw a error, or throw an exception
Default:nan
C++ Type:MooseEnum
Options:nan, nan_warning, error, exception
Controllable:No
Description:What to do if evaluation error occurs. Options are to pass a nan, pass a nan with a warning, throw a error, or throw an exception

Parsed Expression Advanced Parameters

output_propertiesList of material properties, from this material, to output (outputs must also be defined to an output type)
C++ Type:std::vector<std::string>
Controllable:No
Description:List of material properties, from this material, to output (outputs must also be defined to an output type)
outputsnone Vector of output names where you would like to restrict the output of variables(s) associated with this object
Default:none
C++ Type:std::vector<OutputName>
Controllable:No
Description:Vector of output names where you would like to restrict the output of variables(s) associated with this object

Outputs Parameters

prop_getter_suffixAn optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
C++ Type:MaterialPropertyName
Unit:(no unit assumed)
Controllable:No
Description:An optional suffix parameter that can be appended to any attempt to retrieve/get material properties. The suffix will be prepended with a '_' character.
use_interpolated_stateFalseFor the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.
Default:False
C++ Type:bool
Controllable:No
Description:For the old and older state use projected material properties interpolated at the quadrature points. To set up projection use the ProjectedStatefulMaterialStorageAction.

Material Property Retrieval Parameters

Input Files

(test/tests/mox_pore_velocity/MOXPoreVelocityVaporPressure.i)

References

Yoshihisa Ikusawa, Takayuki Ozawa, Shun Hirooka, Koji Maeda, Masato Kato, and Seiichiro Maeda. Development and verification of the thermal behavior analysis code for ma containing mox fuels. In International Conference on Nuclear Engineering. Prague, Czech Republic, July 7–11 2014.

@inproceedings{ikusawa_icone_2014,
    Author = "Ikusawa, Yoshihisa and Ozawa, Takayuki and Hirooka, Shun and Maeda, Koji and Kato, Masato and Maeda, Seiichiro",
    Title = "Development and Verification of the Thermal Behavior Analysis Code for MA Containing MOX Fuels",
    Year = "2014",
    Booktitle = "International Conference on Nuclear Engineering",
    Month = "July 7--11",
    Address = "Prague, Czech Republic"
}

(test/tests/mox_pore_velocity/MOXPoreVelocityVaporPressure.i)

# This input files uses the pore difusion kernels

[UserObjects]
  [pin_geometry]
    type = Layered1DFuelPinGeometry
    include_clad = false
    mesh_generator = layered1D_mesh
  []
[]

[Mesh]
  coord_type = RZ
  [layered1D_mesh]
    type = Layered1DMeshGenerator
    fuel_height = 0.1
    pellet_outer_radius = 0.0041
    include_clad = false
    pellet_bottom_coor = 0.0
    pellet_mesh_density = customize
    nx_p = 200
    elem_type = EDGE2
    slices_per_block = 1
    include_plenum = false
  []
[]

[Variables]
  [temperature]
    initial_condition = 1400.0
  []
  [pore]
    initial_condition = 0.12
    scaling = 1e14
  []
[]

[AuxVariables]
  [pore_speed_aux]
    order = constant
    family = monomial
  []
  [fission_rate_aux_variable_mox]
    order = first
    family = lagrange
  []
[]

[Functions]
  [power_history1]
    type = PiecewiseLinear
    x = '0 10000'
    y = '0 50000'
  []
[]

[Kernels]

  [heat] # gradient term in heat conduction equation
    type = HeatConduction
    variable = temperature
  []
  [heat_ie] # time term in heat conduction equation
    type = HeatConductionTimeDerivative
    variable = temperature
  []
  [heat_source] # source term in heat conduction equation
    type = NeutronHeatSource
    variable = temperature
    block = fuel # fission rate applied to the fuel (block 2) only
    fission_rate = fission_rate_aux_variable_mox
  []

  [pore_diffusion]
    type = MOXPoreDiffusion
    variable = pore
    debug = 0
    # nu = 3.25e-8 #seems to be THE value to use... result is super sensitive to this number
    # nu = 10e-10
    nu = 1e-12
    heating_function = power_history1
    v_upper = 1e-12
    v_lower = 1e-20
    # v_upper = 1
    # v_lower = 1
  []

  [pore_continuity]
    type = MOXPoreContinuity
    variable = pore
    temperature = temperature
    debug = 0
    alpha = 0.25
    beta = 1
    heating_function = power_history1
  []
  [poretimederivative]
    type = CoefTimeDerivative
    variable = pore
    Coefficient = 1
  []
[]

[AuxKernels]
  [pore_speed_aux]
    type = MaterialRealAux
    variable = pore_speed_aux
    property = pore_velocity
    block = fuel
    execute_on = 'initial timestep_end'
  []
  [fission_rate_aux_kernel_mox]
    type = FissionRateGeneral
    fission_rate_formulation = MOX
    variable = fission_rate_aux_variable_mox
    block = fuel
    porosity = pore
    initial_porosity = 0.12
    rod_ave_lin_pow = power_history1
    pellet_diameter = 0.0082
    pellet_inner_diameter = 0
    energy_per_fission = 3.2e-11
    execute_on = 'initial timestep_end'
  []
[]

[BCs]
  [temp_outside] # pin pellets and clad along axis of symmetry (y)
    type = DirichletBC
    variable = temperature
    boundary = 10
    value = 1400
  []
[]

[Materials]
  [fuel_thermal]
    type = MAMOXThermal
    block = fuel
    temperature = temperature
    porosity = pore
    porosity_limit = 0.9
  []
  [density_block]
    type = GenericConstantMaterial
    block = fuel
    prop_names = density
    prop_values = 10431.0
  []
  [pore_velocity]
    type = MOXPoreVelocityVaporPressure
    block = fuel
    temperature = temperature
    scale_factor = 1e0
    # limit = 1e-3
    # scale_factor = 0.05 # go back to this if necessary
    # scale_factor = 0.1
    # oxygen_partial_pressure = PO2
  []
  [oxygen_partial_pressure_integral]
    type = MOXOxygenPartialPressure
    block = fuel
    temperature = temperature
    o2m_deviation = 0.02
    po2_initial = 0.01
    outputs = exodus
    # type = GenericConstantMaterial
    # block = fuel
    # prop_names = PO2
    # prop_values = 1.0
  []
  [Sum]
    type = MOXVaporPressure
    temperature = temperature
    block = fuel
    evalerror_behavior = error
    outputs = exodus
  []
[]

[Dampers]
  [limitT]
    type = MaxIncrement
    max_increment = 100.0
    variable = temperature
  []
[]

[Executioner]
  type = Transient
  solve_type = 'PJFNK'
  snesmf_reuse_base = false

  petsc_options = '-snes_ksp_ew'
  petsc_options_iname = '-pc_type -pc_factor_mat_solver_package' # -mat_superlu_dist_fact'
  petsc_options_value = 'lu superlu_dist' # SamePattern_SameRowPerm'

  line_search = 'none'

  l_max_its = 50
  l_tol = 8e-3
  nl_max_its = 25
  nl_rel_tol = 1e-5
  nl_abs_tol = 1e-8 #1e-10
  n_startup_steps = 1
  end_time = 1.5e5
  num_steps = 2
  dtmax = 1000
  dtmin = 1

  [TimeStepper]
    type = IterationAdaptiveDT
    dt = 2e2
    optimal_iterations = 8
    iteration_window = 2
    linear_iteration_ratio = 100
    growth_factor = 2
    cutback_factor = .5
    force_step_every_function_point = true
    timestep_limiting_function = power_history1
  []
[]

[Postprocessors]
  [_dt] # time step
    type = TimestepSize
  []
  [z_nonlinear_its] # number of nonlinear iterations at each timestep
    type = NumNonlinearIterations
  []
  [power_input]
    type = FunctionValuePostprocessor
    function = power_history1
    scale_factor = 0.1 # rod height
  []

  [rod_total_power_mox]
    type = LayeredElementIntegralPowerPostprocessor
    variable = temperature
    block = fuel
    fission_rate = fission_rate_aux_variable_mox
    fuel_pin_geometry = pin_geometry
  []

  [ave_fuel_temp]
    type = ElementAverageValue
    block = fuel
    variable = temperature
  []
  [max_fuel_temp]
    type = NodalExtremeValue
    block = fuel
    value_type = max
    variable = temperature
  []

  [ave_pore]
    type = ElementAverageValue
    block = fuel
    variable = pore
  []
  [max_pore]
    type = NodalExtremeValue
    block = fuel
    value_type = max
    variable = pore
  []
  [min_pore]
    type = NodalExtremeValue
    block = fuel
    value_type = min
    variable = pore
  []
  [max_pore_speed]
    type = ElementExtremeValue
    block = fuel
    value_type = max
    variable = pore_speed_aux
  []
  [center_PO2]
    type = ElementalVariableValue
    elementid = 0
    variable = PO2
  []
[]

# The MOX capabilities are under active development and the blocks below are useful for
# development and debugging by providing the profiles of the desired quantities.
# They are commented out for the tests, as it would unnecessarily increase computational costs
# and memory requirements.
# [VectorPostprocessors]
#   [line_value_vector_postprocessor_pore]
#     type = LineValueSampler
#     variable = pore
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#     control_tags = a
#   []
#   [line_value_vector_postprocessor_pore_speed]
#     type = LineValueSampler
#     variable = pore_speed_aux
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
#   [line_value_vector_postprocessor_temperature]
#     type = LineValueSampler
#     variable = temperature
#     start_point = '0.0 0.05 0'
#     end_point = '0.0041 0.05 0'
#     num_points = 100
#     sort_by = x
#     execute_on = linear
#     outputs = stuff_v_rad
#   []
# []

[Outputs]
  exodus = true
  csv = false
  color = false
  [console]
    type = Console
    max_rows = 25
    all_variable_norms = true
  []
  # [stuff_v_rad]
  #   type = CSV
  #   execute_on = 'FINAL'
  # []
[]

[Debug]
  show_var_residual_norms = true
[]

Description
Input Parameters
Input Files
References